On inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations

• Date: 2015
• Main Authors: Catarino, Paula, Higgins, Peter M., Levi, Inessa
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2015
• Subjects: semigroup; semilattice; inverse subsemigroup; strong inverse; transformation; order-preserving transformation; orientation-preserving transformation; orientation-reversing transformation; 20M20; 05C25
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/43
• Journal Title: Algebra and Discrete Mathematics

It is well-known [16] that the semigroup \(\mathcal{T}_n\) of all total transformations of a given \(n\)-element set \(X_n\) is covered by its inverse subsemigroups. This note provides a short and direct proof, based on properties of digraphs of transformations, that every inverse subsemigroup of or...